can you please reword this?
Let m and n be lines that intersect line a. Let m be perpendicular to a. This means that all 4 of the angles formed by the intersection of m and a are 90°.
Let n be perpendicular to a. This means that all 4 of the angles formed by the intersection of n and a are also 90°.
Since all of the angles are congruent, this means that the same-side interior angles (between lines m and n) are congruent. If two same-side interior angles are congruent, then the lines are parallel
Assume lines m and n intersect line a. Line m is perpendicular to line a, indicating that all four angles formed by the intersection of m and a are 90°.
Likewise, line n is perpendicular to line a, meaning that all four angles formed by the intersection of n and a are also 90°.
As all angles are equal, this implies that the same-side interior angles (between lines m and n) are also equal. When two same-side interior angles are equal, the lines are parallel.
Reworded:
Consider lines m and n intersecting line a. Assume m is perpendicular to a, indicating that all four angles formed by the intersection of m and a measure 90°.
Similarly, suppose n is also perpendicular to a, implying that all four angles formed by the intersection of n and a also measure 90°.
As all the angles are equal, it follows that the same-side interior angles (between lines m and n) are congruent. Therefore, if two same-side interior angles are congruent, the lines m and n are parallel.
Certainly! Here's a reworded version:
Consider three lines: m, n, and a. Line a intersects with both m and n. Suppose that line m is perpendicular to line a, meaning that all four angles formed at the intersection of m and a measure 90°. Similarly, line n is also perpendicular to line a, implying that all four angles formed at the intersection of n and a are also 90°.
Since all the angles are equal, it follows that the same-side interior angles (those between lines m and n) are also equal. In other words, the angles formed by the intersection of m and a on one side are congruent to the angles formed by the intersection of n and a on the same side. If two same-side interior angles are congruent, then the lines m and n are parallel to each other.